VITEEE Examination Previous Year Question Paper 2017 With Answer Key

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VITEEE Question Paper-2017

Part I (Physics)

1. A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20 m/s2, the amount of gas ejected per second to supply the needed thrust will be (Take g = 10 m/s2)

(a)  127.5 kg/s

(b)  137.5 kg/s

(c)  155.5 kg/s

(d)  187.5 kg/s

Answer: (d)

2. The power dissipated in the circuit shown in the figure is 30 Watts. The value of R is

(a)  20 Ω

(b)  15 Ω

(c)  10 Ω

(d)  30 Ω

Answer: (c)

3. If the kinetic energy of a moving particles is E, then the de-Broglie wavelength is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

4. Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of linear momentum of B to A is

(a)  1 : 3

(b)  3 : 1

(c)  1 : √3

(d)  √3 : 1

Answer: (c)

5. In which sequence the radioactive radiations are emitted in the following nuclear reaction ?

ZXAZ + 1YAZ – 1KA – 4 Z – 1KA – 4

(a)  γ, α, β

(b)  α, β, γ

(c)  β, γ, α

(d)  β, α, γ

Answer: (d)

6. Which of the following does not support the wave nature of light?

(a)  Interference

(b)  Diffraction

(c)  Polarization

(d)  Photoelectric effect

Answer: (d)

7. Six identical conducting rods are joined as shown in figure. Points A and D are maintained at 200℃ and 20℃ The temperature of junction B will be

(a)  120℃

(b)  100℃

(c)  140℃

(d)  80℃

Answer: (c)

8. A hydrogen atom is in ground state. Then to get six lines in emission spectrum, wavelength of incident radiation should be

(a)  800 Å

(b)  825 Å

(c)  975 Å

(d)  1025 Å

Answer: (c)

9. A conducting circular loop of radius r carries a constant current i. It is placed in a uniform magnetic field  such that  is perpendicular to the plane of the loop. The  magnetic force acting on the loop is

(a)  ir B0

(b)  2π ir B0

(c)  zero

(d)  π ir B0

Answer: (c)

10. A vessel of depth 2d cm is half filled with a liquid of refractive index μ1 and the upper half with a liquid of refractive index μ2. The apparent depth of the vessel seen perpendicularly is

(a) 

(b) 

(c) 

(d) 

Answer: (b)

11. A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision, their final velocities are V and v respectively. The value of v is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

12. Two capacitors C1 and C2 in a circuit are joined as shown in figure. The potentials of points A and B are V1 and V2 Then the potential of point D will be

(a) 

(b) 

(c) 

(d) 

Answer: (c)

13. Light of wavelength 500 nm is incident on a metal with work function 2.28 eV. The de Broglie wavelength of the emitted electron is :

(a)  < 2.8 × 109 m

(b)  ≥ 2.8 × 109 m

(c)  ≤ 2.8 × 1012 m

(d)  < 2.8 × 1010 m

Answer: (b)

14. Kerosene oil rises up in a wick of a lantern because of

(a)  diffusion of the oil through the wick

(b)  capillary action

(c)  buoyant force of air

(d)  the gravitational pull of the wick

Answer: (b)

15. The current in a coil of L = 40 mH is to be increased uniformly from 1A to 11 A in 4 milli sec. The induced e.m.f. will be

(a)  100 V

(b)  0.4 V

(c)  440 V

(d)  40 V

Answer: (a)

16. An alternative voltage of 220 V, 50 Hz frequency is applied across a capacitor of capacitance 2 μ The impedance of the circuit is

(a) 

(b) 

(c)  500 π

(d) 

Answer: (d)

17. The combination of gates shown below yields

(a)  OR gate

(b)  NOT gate

(c)  XOR gate

(d)  NAND gate

Answer: (a)

18. A hollow insulated conduction sphere is given a positive charge of 10 μ What will be the electric field at the centre of the sphere if its radius is 2 metres?

(a)  Zero

(b)  5 μCm2

(c)  20 μCm2

(d)  8 μCm2

Answer: (a)

19. Two mercury drops (each of radius r) merge to form a bigger drop. The surface energy of the bigger drop, if T is the surface tension, is

(a)  25/3 πr2T

(b)  4 πr2T

(c)  2 πr2T

(d)  28/3 πr2T

Answer: (d)

20. Resistances 1 Ω, 2 Ω and 3 Ω are connected to form a triangle. If a 1.5 V cell of negligible internal resistance is connected across the 3 Ω resistor, the current flowing through this resistor will be

(a)  0.25 A

(b)  0.5 A

(c)  1.0 A

(d)  1.5 A

Answer: (b)

21. A current carrying coil is subjected to a uniform magnetic field. The coil will orient so that its plane becomes

(a)  inclined at 45° to the magnetic field

(b)  inclined at any arbitrary angle to the magnetic field

(c)  parallel to the magnetic field

(d)  perpendicular to the magnetic field

Answer: (d)

22. The value of tan (90° − θ) in the graph gives

(a)  Young’s modulus of elasticity

(b)  compressibility

(c)  shear strain

(d)  tensile strength

Answer: (a)

23. An electron makes a transition from an excited state to the ground state of hydrogen – like atom. Then

(a)  kinetic energy decreases, potential energy increases but total energy remains same

(b)  kinetic energy and total energy decrease but potential energy increases

(c)  its kinetic energy increases but potential energy and total energy decrease

(d)  kinetic energy, potential energy and total energy decrease

Answer: (c)

24. An A.C. source is connected to a resistive circuit. Which of the following is true?

(a)  Current leads ahead of voltage in phase

(b)  Current lags behind voltage in phase

(c)  Current and voltage are in same phase

(d)  Any of the above may be true depending upon the value of resistance.

Answer: (c)

25. A milli voltmeter of 25 milli volt range is to e converted into an ammeter of 25 ampere range. The value (in ohm) of necessary shunt will be

(a)  0.001

(b)  0.01

(c)  1

(d)  0.05

Answer: (a)

26. In young’s double-slit experiment, the intensity of light at a point on the screen where the path difference is λ is I, λ being the wavelength of light used. The intensity at a point where the path difference is λ/4 will be

(a)  I/4

(b)  I/2

(c)  I

(d)  zero

Answer: (b)

27. Which of the following is a self adjusting force?

(a)  Static friction

(b)  Limiting friction

(c)  Dynamic friction

(d)  Sliding friction

Answer: (a)

28. Which of the following are not electromagnetic waves?

(a)  Cosmic rays

(b)  Gamma rays

(c)  β-rays

(d)  X-rays

Answer: (a)

29. Graph of specific heat at constant volume for a monatomic gas is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

30. A charge +q is at a distance L/2 above a square of side L. Then what is the flux linked with the surface?

(a)  q/4ε0

(b)  2q/3ε0

(c)  q/6ε0

(d)  6q/ε0

Answer: (c)

31. The potential energy of a system increases if work is done

(a)  upon the system by a non conservative force

(b)  by the system against a conservative force

(c)  by the system against a non conservative force

(d)  upon the system by a conservative force

Answer: (d)

32. Two capacitors when connected in series have a capacitance of 3 μF, and when connected in parallel have a capacitance of 16 μ Their individual capacities are

(a)  1 μF, 2 μF

(b)  6 μF, 2 μF

(c)  12 μF, 4 μF

(d)  3 μF, 16 μF

Answer: (c)

33. Resonance frequency of LCR series a.c. circuit is f0. Now the capacitance is made 4 times, then the new resonance frequency will become

(a)  f0/4

(b)  2f0

(c)  f0

(d)  f0/2.

Answer: (d)

34. If the light is polarized by reflection, then the angle between reflected and refracted light is

(a)  180°

(b)  90°

(c)  45°

(d)  36°

Answer: (b)

35. The velocity of efflux of a liquid through an orifice in the bottom of the tank does not depend upon

(a)  size of orifice

(b)  height of liquid

(c)  acceleration due to gravity

(d)  density of liquid

Answer: (a)

36. On a smooth plane surface (figure) two block A and B are accelerated up by applying a force 15 N on A. If mass of B is twice that of A, the force on B is

(a)  30 N

(b)  15 N

(c)  10 N

(d)  5 N

Answer: (c)

37. A potentiometer wire, 10 m long, has a resistance of 40Ω. It is connected in series with a resistance box and a 2 V storage cell. If the potential gradient along the wire 0.1 m is V/cm, the resistance unplugged in the box is

(a)  260 Ω

(b)  760 Ω

(c)  960 Ω

(d)  1060 Ω

Answer: (b)

38. A prism has a refracting angle of 60°. When placed in the position of minimum deviation, it produces a deviation of 30°. The angle of incidence is

(a)  30°

(b)  45°

(c)  15°

(d)  60°

Answer: (b)

39. Transfer characteristics [output voltage (V0) vs input voltage (Vi)] for a base biased transistor in CE on configuration is as shown in the figure. For using transistor as a switch,, it is used

(a)  in region (III)

(b)  both in region (I) and (III)

(c)  in region (II)

(d)  in region (I)

Answer: (b)

40. A bar magnet of magnetic moment M, is placed in a magnetic field of induction B. The torque exerted on it is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

PART – II (CHEMISTRY)

41. Schottky defect in crystals is observed when

(a)  unequal number of cations and anions are missing from the lattice

(b)  equal number of cations and anions are missing from the lattice

(c)  an ion leaves its normal site and occupies an interstitial site

(d)  density of the crystal is increased

Answer: (b)

42. The cyclobutyl methylamine with nitrous acid gives

(a) 

(b) 

(c) 

(d)  All of these

Answer: (d)

43. The exothermic formation of CIF3 is represented by the equation :

Cl2(g) + 3F2(g) ⇌ 2ClF3­(g); ∆H = −329 kJ

Which of the following will increase the quantity of CIF3 in an equilibrium mixture of Cl2, F2 and CIF3?

(a)  Adding F2

(b)  Increasing the volume of the container

(c)  Removing Cl2

(d)  Increasing the temperature

Answer: (a)

44. For the reaction 2NO2(g) ⇌ 2NO(g) + O2(g)

(Kc = 1.8 × 106 at 184℃) (R = 0.0831 kJ/(mol.K)

When Kp and K­c are compared at 184℃, it is found that

(a)  Whether Kp is greater than, less than or equal to Kc depends upon the total gas pressure

(b)  Kp = Kc

(c)  Kp is less than Kc

(d)  Kp is greater than Kc

Answer: (d)

45. 

(a) 

(b) 

(c) 

(d) 

Answer: (b)

46. A compound MpXq has cubic close packing (ccp) arrangement of X. If unit cell structure is shown below. The empirical formula of the compound is

(a)  MX

(b)  MX2

(c)  M2X

(d)  M5X14

Answer: (b)

47. What is Z in the following sentences of reactions?

(a)  Benzene

(b)  Toluene

(c)  Benzaldehyde

(d)  Benzoic acid

Answer: (c)

48. Which of the following oxy-acids has the maximum number of hydrogens directly attached to phosphorus?

(a)  H4P2O7

(b)  H3PO2

(c)  H3PO3

(d)  H3PO4

Answer: (b)

49. The number of geometrical isomers of CH3CH=CH−CH=CH−CH=CHCl is

(a)  2

(b)  4

(c)  6

(d)  8

Answer: (d)

50. If ‘a’ stand for the edge length of the cubic systems : simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these systems will be respectively,

(a) 

(b) 

(c) 

(d) 

Answer: (a)

51. For a first order reaction A → P, the temperature (T) dependent rate constant (k) was found to follow the equation  The pre-exponential factor A and the activation energy Ea, respectively, are

(a)  1.0 × 106 s1 and 9.2 kJ mol1

(b)  6.0 s1 and 16.6 kJ mol1

(c)  1.0 × 106 s1 and 16.6 kJ mol1

(d)  1.0 × 106 s1 and 38.3 kJ mol1

Answer: (d)

52. 1-Propanol and 2-propanol can be distinguished by

(a)  oxidation with alkaline KMnO4 followed by reaction with Fehling solution

(b)  oxidation with acidic dichromate followed by reaction with Fehling solution

(c)  oxidation by heating with copper followed by reaction with Fehling solution

(d)  oxidation with concentrated H2SO4 followed by reaction with Fehling solution

Answer: (c)

53. Which group contains coloured ions out of

1. Cu2+ 2. Ti4+

3. Co2+ 4. Fe2+

(a)  1, 2, 3, 4

(b)  1, 3, 4

(c)  2, 3

(d)  1, 2

Answer: (b)

54. The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2 = 0.301)

(a)  23.03 minutes

(b)  46.06 minutes

(c)  460.6 minutes

(d)  230.03 minutes

Answer: (b)

55. A mixture of benzaldehyde and formaldehyde on heating with aqueous NaOH solution gives

(a)  benzyl alcohol and sodium formate

(b)  sodium benzoate and methyl alcohol

(c)  sodium benzoate and sodium formate

(d)  benzyl alcohol and methyl alcohol

Answer: (a)

56. In the following reaction sequence, the correct structures of E, F and G are

 

(a) 

(b) 

(c) 

(d) 

Answer: (c)

57. Standard entropies of X2, Y2 and XY3 are 60, 30 and 50 JK1 mol1 For the reaction  ∆H = −30 kJ to be at equilibrium, the temperature should be:

(a)  750 K

(b)  1000 K

(c)  1250 K

(d)  500 K

Answer: (a)

58. An organic compound (A) on reduction gives compound (B). (B) on treatment with CHCl3 and alcoholic KOH gives (C). (C) on catalytic reduction gives N-methylaniline. The compound A is

(a)  Methylamine

(b)  Nitromethane

(c)  Aniline

(d)  Nitrobenzene

Answer: (d)

59. The standard reduction potential for Cu2+/Cu is +0.34. Calculate the reduction potential at pH = 14 for the above couple. (Ksp Cu(OH)2 = 1 × 1019)

(a)  −0.22 V

(b)  +0.22 V

(c)  −0.44 V

(d)  +0.44 V

Answer: (a)

60. A substance C4H10O yields on oxidation a compound, C4H8O which gives an oxime and positive iodoform test. The original substance on treatment with conc. H2SO4 gives C4H8. The structure of the compound is

(a)  CH3CH2CH2CH2OH

(b)  CH3CHOHCH2CH3

(c)  (CH3)3COH

(d)  CH3CH2−O−CH2CH­3

Answer: (b)

61. The emf of a particular voltaic cell with the cell reaction  is 0.65 V. The maximum electrical work of this cell when 0.5 g of H2 is consumed.

(a)  −3.12 × 104 J

(b)  −1.25 × 105 J

(c)  25.0 × 106 J

(d)  None

Answer: (a)

62. The number of aldol reaction (s) that occurs in the given transformation is:

CH3CHO+4HCHO

(a)  1

(b)  2

(c)  3

(d)  4

Answer: (c)

63. Which of the following is not intermediate in the acid catalyzed reaction of benzaldehyde with 2 equivalent of methanol to give acetal?

(a) 

(b) 

(c) 

(d) 

Answer: (b)

64. Iron crystallizes in several modifications. At about 911℃, the bcc ‘α’ form undergoes a transition to fcc ‘γ’ form. If the distance between the two nearest neighbours is the same in the two forms at the transition temperature, the ratio of the density of iron in fcc form (ρ2) to that of iron of bcc form (ρ1) at the transition temperature

(a) 

(b) 

(c) 

(d) 

Answer: (a)

65. The half life of the first order reaction CH3.CHO (g) → CH4(g) + CO (g)

If initial pressure of CH3CHO (g) is 80 mm Hg and the total pressure at the end of 20 minutes is 120 mm  Hg

(a)  80 min

(b)  120 min

(c)  20 min

(d)  40 min

Answer: (c)

66. A compound is soluble in conc. H2SO4. It does not decolourise bromine in carbon tetrachloride but is oxidized by chromic anhydride in aqueous sulphuric acid within two seconds, turning orange solution to blue, green and then opaque. The original compound is

(a)  a primary alcohol

(b)  a tertiary alcohol

(c)  an alkane

(d)  an ether

Answer: (a)

67. The values of Planck’s constant is 6.63 × 10−34 The velocity of light o s 3.0 × 108 m s−1. Which value is closest to the wavelength in nanometers of a quantum of light with frequency of 8 × 105 s−1?

(a)  5 × 10−18

(b)  4 × 101

(c)  3 × 107

(d)  2 × 10−25

Answer: (b)

68. The number of stereoisomers possible for a compound of the molecular formula CH3−CH=CH−CH(OH)−Me is:

(a)  2

(b)  4

(c)  6

(d)  3

Answer: (b)

69. The optically active tartaric acid is named as D – (+) – tartaric acid because it has a positive

(a)  optical rotation and is drived from D –glucose

(b)  pH in organic solvent

(c)  optical rotation and is derived from D – (+) – glyceraldehyde

(d)  optical rotation when substituted by deuterium

Answer: (c)

70. Consider the reaction : N2 + 3H2 → 2NH3 carried out at constant temperature and pressure. If ∆H and ∆U are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

(a)  ∆H > ∆U

(b)  ∆H < ∆U

(c)  ∆H = ∆U

(d)  ∆H = 0

Answer: (b)

71. What is D in the following sequence of reactions?

(a) 

(b) 

(c) 

(d) 

Answer: (a)

72. Knowing that the chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements is incorrect?

(a)  The ionic size of Ln (III) decrease in general with increasing atomic number

(b)  Ln (III) compounds are generally colourless.

(c)  Ln (III) hydroxide are mainly basic in character.

(d)  Because of the large size of the Ln (III) ions the bonding in its compounds is predominantly ionic in character.

Answer: (b)

73. What is the R and S configuration for each stereogenic centre in this sugar from top to bottom?

(a)  R, R, S

(b)  R, S, S

(c)  R, S, R

(d)  S, S, R

Answer: (c)

74. Saponificatino of coconut oil yields glycerol and

(a)  palmitic acid

(b)  sodium palmitate

(c)  oleic acid

(d)  stearic acid

Answer: (b)

75. A certain reaction is non spontaneous at 298 K. The entropy change during the reaction is 121 JK1. Is the reaction is endothermic or exothermic? The minimum value of ∆H for the reaction is

(a)  endothermic,     ∆H = 36.06 kJ

(b)  exothermic,       ∆H = −36.06 kJ

(c)  endothermic,     ∆H = 60.12 kJ

(d)  exothermic,       ∆H = −60.12 kJ

Answer: (a)

76. p –cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

77. Which of the following has maximum number of lone pairs associated with Xe?

(a)  XeF4

(b)  XeF6

(c)  XeF2

(d)  XeO3

Answer: (c)

78. Which one of the following statements is not true regarding (+) Lactose?

(a)  On hydrolysis (+) Lactose gives equal amount of D (+) glucose and D(+) galactose.

(b)  (+) Lactose is a β-glycoside formed by the union of a molecule of D(+) glucose and molecule of D(+) galactose.

(c)  (+) Lactose is a reducing sugar and does not exhibit mutarotation.

(d)  (+) Lactose, C12H22O11 contains 8-OH groups.

Answer: (c)

79. If one strand of DNA has the sequence ATGCTTGA, the sequence in the complimentary strand would be

(a)  TACGAACT

(b)  TCCGAACT

(c)  TACGTACT

(d)  TACGTAGT

Answer: (a)

80. The starting reagents needed to make the azo compound shown below

(a) 

(b) 

(c) 

(d) 

Answer: (b)

PART – III MATHEMATICS

81. sin1 (sin 5) > x2 – 4x holds if

(a) 

(b) 

(c) 

(d) 

Answer: (d)

82. A value of c for which conclusions of Mean Value Theorem holds for the function f(x) = loge x on the interval [1, 3] is

(a)  log3e

(b)  loge 3

(c)  2 log3 e

(d) 

Answer: (c)

83. Negation of the proposition : If we control population growth, we prosper

(a)  If we do not control population growth, we prosper

(b)  If we control population growth, we do not prosper

(c)  We control population but we do not prosper

(d)  We do not control population, but we prosper

Answer: (c)

84. The equation  represents a circle of radius

(a)  2

(b)  3

(c)  4

(d)  6

Answer: (b)

85. The function f(x) = sin x – kx – c, where k and c are constants, decreases always when

(a)  k > 1

(b)  k ≥ 1

(c)  k < 1

(d)  k ≤ 1

Answer: (b)

86. Equation  represents

(a)  A rectangular hyperbola

(b)  A hyperbola

(c)  An ellipse

(d)  A parabola

Answer: (b)

87. The acceleration of a sphere falling through a liquid is (30 – 3v) cm/s2 where v is its speed in cm/s. The maximum possible velocity of the sphere and the time when it is achieved are

(a)  10 cm/s after 10 second

(b)  10 cm/s instantly

(c)  10 cm/s, will never be achieved

(d)  30 cm/s, after 30 second

Answer: (c)

88. A straight line parallel to the line 2x – y + 5 = 0 is also a tangent to the curve y2 = 4x + 5. Then the point of contact is

(a)  (2, 1)

(b)  (−1, 1)

(c)  (1, 3)

(d)  (3, 4)

Answer: (b)

89. Value of  is

(a)  π/2

(b)  −π/2

(c)  π/4

(d)  None of these

Answer: (c)

90. The range of the function  is

(a)  (−2, ∞)

(b)  [−2, 3]

(c)  [1/3, 1]

(d)  (1/2, 1)

Answer: (c)

91. The area bounded by y – 1 = |x|, y = 0 and |x| = 1/2 will be :

(a)  3/4

(b)  3/2

(c)  5/4

(d)  None of these

Answer: (c)

92. The value of x obtained from the equation  will be

(a)  0 and –(α + β + γ)

(b)  0 and α + β + γ

(c)  1 and (α – β – γ)

(d)  0 and α2 + β2 + γ2

Answer: (a)

93. The solution of the differential equation  is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

94. 

(a)  1/3

(b)  2/3

(c)  −2/3

(d)  2/9

Answer: (d)

95. If  then which of the following is always true?

(a)  are necessarily coplanar

(b)  either  must lie in the plane of 

(c)  either  must lie in the plane of 

(d)  either  must lie in the plane of 

Answer: (c)

96. Let A be the centre of the circle x2 + y2 – 2x – 4y – 20 = 0, and B(1, 7) and D(4, −2) are points on the circle then, if tangents be drawn at B and D, which meet at C, then area of quadrilateral ABCD is –

(a)  150

(b)  75

(c)  75/2

(d)  None of these

Answer: (b)

97. is equal to :

[Given f(0) = g(0) = 0]

(a)  f(1) g(1) – f(1)g’ (1)

(b)  f(1) g’ (1) + f’ (1) g(1)

(c)  f(1) g’ (1) – f’(1) g(1)

(d)  none of these

Answer: (c)

98. If  then z14 =

(a)  27

(b)  27 i

(c)  214 i

(d)  −27 i

Answer: (d)

99. The difference between greatest and least value of f(x) = 2 sin x + sin 2x,  is-

(a) 

(b) 

(c) 

(d) 

Answer: (c)

100. A and B are two independent witnesses (i.e. there is no collision between them) in a case. The probability that A will speak the truth is x and the probability that B will speak the truth is y. A and B agree in a certain statement. The probability that the statement is true is

(a) 

(b) 

(c) 

(d) 

Answer: (d)

101. A and B are events such that P (A ∪ B) = 3/4; P (A ∩ B) = 1/4,  is

(a)  5/12

(b)  3/8

(c)  5/8

(d)  1/4

Answer: (a)

102. The line which passes through the origin and intersect the two lines  is

(a) 

(b) 

(c) 

(d) 

Answer: (a)

103. If  then un + un – 2 is :

(a) 

(b) 

(c) 

(d) 

Answer: (a)

104. Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

(a)  69760

(b)  30240

(c)  99784

(d)  None of these

Answer: (a)

105. The area bounded by f(x) = x2, 0 ≤ x ≤ 1, g(x) = −x + 2, 1 ≤ x ≤ 2 and x-axis is

(a)  3/2

(b)  4/3

(c)  8/3

(d)  None of these

Answer: (d)

106. The condition that the line  be a normal to the parabola y2 = 4axn is]

(a)  p3 = 2ap2 + aq2

(b)  p3 = 2aq2 + ap2

(c)  q3 = 2ap2 + aq2

(d)  None of these

Answer: (a)

107. A random variable X ha the probability distribution

For the events E ={X is a prime number} and F = {X < 4}, then P(E ∪ F) is

(a)  0.50

(b)  0.77

(c)  0.35

(d)  0.87

Answer: (b)

108. The value of  is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

109. The parabola having its focus at (3, 2) and directrix along the y-axis hass its vertex at

(a)  (2, 2)

(b)  (3/2, 2)

(c)  (1/2, 2)

(d)  (2/3, 2)

Answer: (b)

110. The rank of the matrix  is

(a)  1 if a = 6

(b)  2 if a= 1

(c)  3 if a = 2

(d)  1 if a = 4

Answer: (b)

111. If  then  is equal to

(a)  1/4

(b)  −1/3

(c)  1/2

(d)  1

Answer: (b)

112. The distance of the point (1, −2, 3) from the plane x – y + z = 5 measured parallel to the line  is

(a)  1

(b)  2

(c)  4

(d)  2√3

Answer: (a)

113. The tangent lines to the curve y2 = 4ax at points where x = a, are

(a)  parallel

(b)  perpendicular

(c)  inclined at 60°

(d)  inclined at 30°

Answer: (b)

114. If the eccentricity of the hyperbola x2 – y2 cosec2 α = 25 is √5 times the eccentricity of the ellipse x2 cosec2 α + y2 = 5, then α is equal to :

(a) 

(b) 

(c) 

(d) 

Answer: (a)

115. The conditional (p ⋀ q) ⇒ p is

(a)  A tautology

(b)  A fallacy i.e, contradiction

(c)  Neither tautology nor fallacy

(d)  None of these

Answer: (a)

116. The set of points of discontinuity of the function  is given by

(a)  R

(b) 

(c) 

(d)  None of these

Answer: (c)

117. The volume V and depth x of water in a vessel are connected by the relation  the volume of water is increasing, at the rate of 5 cm3/sec, when x = 2 cm. The rate at which the depth of water is increasing, is

(a) 

(b) 

(c) 

(d) 

Answer: (d)

118. If vectors  and  (a ≠b ≠ c ≠ 1) are coplanar,, then find 

(a)  0

(b)  1

(c)  −1

(d)  2

Answer: (b)

119. If matrix  and  then k is

(a)  7

(b)  −7

(c)  15

(d)  −11

Answer: (c)

120. The angle between a pair of tangents drawn from a point T to the circle x2 + y2 + 4x – 6y + 9 sin2 α + 13 cos2 α = 0 is 2α. The equation of the locus of the point T is

(a)  x2 + y2 + 4x – 6y + 4 = 0

(b)  x2 + y2 + 4x – 6y – 9 = 0

(c)  x2 + y2 + 4x – 6y – 4 = 0

(d)  x2 + y2 + 4x – 6y + 9 = 0

Answer: (d)

PART – IV ENGLISH

Directions (Qs. 121-123) Study the paragraph and answer the questions that follow:

At this stage of civilization, when many nations are brought into close and vital contact for good and evil, it is essential, as never before, that their gross ignorance of one another should be diminished, that they should begin to understand a little of one another’s historical experience and resulting mentality. It is the fault of the English to expect the people of other countries to react as they do, to political and international situations. Our genuine goodwill and good intentions are often brought to nothing, because we expect other people to be like us. This would be corrected if we knew the history, not necessarily in detail but in broad outlines, of the social and political conditions which have given to each nation its present character.

121. The character of a nation is the result of its

(a)  gross ignorance

(b)  cultural heritage

(c)  socio-political conditions

(d)  mentality

Answer: (c)

122. According to the author Mentality’ of a nation is mainly product of its

(a)  present character

(b)  international position

(c)  politics

(d)  history

Answer: (d)

123. The need for a greater understanding between nations

(a)  is more today than ever before

(b)  was always there

(c)  is no longer there

(d)  will always be there

Answer: (a)

Directions (Q. 124) : In the question below a sentence is given, a part of which is printed in bold and underline. This part may contain a grammatical error. Each sentence is followed by phrases a, b, c and d. Find out which phrase should replace the phrase given in bold/underline to correct the error, if there is any to make the sentence grammatically meaningful and correct.

124. There are any number of skilled writers who can develop content and create marketing materials with a keen eye to using proven methods, but also to developing new and innovative techniques.

(a)  with a keen eye to using proven methods, but also to developing new and innovative techniques.

(b)  with a keen eye for using proven methods, and also to developing new and innovative techniques.

(c)  with a keen eye not only to using proven methods, but also to developing new and innovative techniques.

(d)  with a keen eye to using prove methods, but to developing new and innovative techniques.

Answer: (c)

125. Choose the best pronunciation of the word, Sorbet from the following options.

(a)  Sore-bet

(b)  Sore-bay

(c)  Sorb rhymes with orb

(d)  Shore-bay

Answer: (b)